Not Chinese fan palm (Livistona chinensis), as that does not have the frond stalks split at the base like your palm. I suspect a Sabal sp., possibly S. mauritiiformis.
Sabal spp. generally are known as palmettos (palmettoes?) in the US, but there seems to be no specific common name for S. mauritiiformis. I only suggested this species because it has a more slender, self-cleaning trunk in relation to its crown size than other Sabal spp. -- but it's still just a guess without seeing more detail of frond and flowering branch. If you really want to get interested in palms it's best to learn the botanical names. Many of the common names the US nursery trade has come up with are silly, pointless and confusing.
Hi Tony, I am in Qld Australia and just trying to identify palms in our recently purchased property. Complete plant dummies. But your help is very welcome. Kind regards, Paula
Tony, It also is dropping lots of "NUTS" at the moment. seem to be coming in droves. I could post other pictures if this would help? P
Not "Mauritius-shaped" but "Mauritia-shaped". One of my books tells me the palm genus Mauritia was named after an 18th C. Dutch governor, Johan Mauritz van Nassau-Siegen.
Alex, I don't think it can be Bismarckia nobilis, but I have also become highly doubtful that it's Sabal mauritiiformis. Bismarckia has bluish-white frond stalks (petioles) and the blades of the fronds are much paler and stiffer as well. The way older fronds in Daisy's picture appear to weaken and collapse at the base of the blade is much more like Sabal. But I could not even be sure it's a Sabal.
It might have helped with the I.D. if the photo had been taken with the sun on the leaves. (Perhaps later in the day with the sun behind the photographer). However, if the frond (leaf) has a deep central 'V', in its surface, i.e., the leaf is not flat from one side to the other, then I would bet on Sabal.
Well, that seems to pin it down! I have to admit that Alex seems to be right. The combination of large fan leaves and those fingerlike inflorescence branches with densely overlapping scales put it without doubt in the borassoid tribe of palms, which includes the genera Borassus, Borassodendron, Latania, Lodoicea, Hyphaene and Bismarckia (also Medemia and Satranala, both hardly known in cultivation). Among the cultivated ones, only Bismarckia has smallish, stalked fruit like this. Genera Palmarum describes them as being "ellipsoidal, ovoid or rounded . . . epicarp [skin] smooth, shiny, rich brown, somewhat speckled with lighter brown . . . endocarp [stone] thick, irregularly flanged and pitted . . ." Their drawings, with scale specified, show a fruit about 3.5 cm diameter. You could check any fallen fruit, Daisy, to see if this description is confirmed. It does appear to have unusually green foliage for a Bismarckia.