The (old) name of this mountain is also Tritthorn and can be found on some Swiss maps.
The popularity of Pizzo Centrale for sure originates in the nice panorama it offers. The summit has really a central position, rising in the ridge which divides the southern valleys of Ticino/Tessin and the central Swiss valley around Andermatt. Its popularity goes also to the proximity of one of the most importand high road passes over Alps - San Gottardo / St Gotthard, 2091 m. After overcoming it, you've done passing the Alps, while most of other passes bring you into a valley from which you must overcome another pass to cross the whole chain of Alps. The traffic over San Gottardo / St Gotthard is dense and also all the three roads are very picturesque. The highway of course the least (but is the fastest), the normal road is quick and nice and the old "La Tremola" is a pearl of past road engineering. While crossing San Gottardo / St Gotthard you can visit many places of high historical value - too many to mention them all. So, devote for a simple drive over the pass a whole day and do a lot of stops to see the nearby landmarks.
A half day hike up on Pizzo Centralle will take you into a touristically quite developed mountain area around the artificial Lago della Sella and then by a sufficiently well marked, but not just trivial and easy path on the panoramic summit. Above, you are on your own and the nature is still completely unspoiled. If you have some imagination, you can even start searching off the path for crystals, embedded in the St. Gotthard granite. In times of tour skiing the slopes from Guspissattel down to the Sella lake are done also with skis.
Just NE of San Gottardo / St Gotthard Monte Prosa, 2737 m is rising. From it towards the NE the ridge goes to the Point 2782, where it branches. Towards the E the ridge continues on Sellaboedeli, 2828 m, then to Gamsspitz, 2925 m, and finally further towards the NE on Pizzo Centrale. And from the highest peak the ridge continues towards the east - over the East foresummit, 2986 m, and further towards the east and southeast. The narrow group of Pizzo Centrale ends on Rotstockluecke (saddle), 2785 m. From the main ridge (from Gamsspitz and East peak) weaker south ridges go, and among them in high basins there are a few smaller lakes. Southeast of Pizzo Centrale there is a big artificial Lago della Sella, 2256 m. The northern side of the main ridge is wilder and not so much visited. Just north of the main summit there is a smaller glacier, called Ober Schatzfirn.
Approacher from other sides are much longer. A quite popular trail is passing by Pizzo Centrale, connecting San Gottardo / St Gotthard with the summit of Gemsstock, 2961 m, which a cable car from Andermatt reaches. But from that path (going over the notch by Gloggentuermli) rarely anybody would do a side jump on Pizzo Centrale. Northeast of Pizzo Centrale there is the valley end of Unteralp valley, which can be also reached from Andermatt. There the Vermigelhuette stands, 2042 m, but the ascent from there on Pizzo Centrale would for normal hikers again go much around (over Passo della Sella) and then by a mostly pathless terrain on top.
See a detailed on-line map here.
The mountain ridges are sharp, but still not sharp enough to prevent skilled mountaineers to scramble by various routes on top. If one would follow the ridges from the west or from the east, the difficulty of routes would be T5 (by the Swiss Hiking Scale), with some easy climbing details of UIAA II difficulty.
In times of tour skiing people don't follow the normal route. They go instead till the end of Sella lake (till Capanna di Val Torta) and there turn north. Quite steep slopes bring them directly below the southern ridge of Gamsspitz, then they cross it and follow the normal route on top. The last 100 meters of altitude you would normally do on foot.
In winter condition the ascent requires ice pick and crampons and if icy on top also other measures of security. For a ski tour the southern slopes of the mountain must be safe of avalanches, because they are quite steep.