I have experience with ASCOM and I am beginner on stellar mate. In ASCOM the user can generate a stars model so that when the telescope is switched on, at the first pointing the object is more or less in the CCD FOV. With stellarmate I have to perform the star alignment every time in different nights because the first telescope pointing error is always quite relevant. I am wondering if there is stellarmate a mechanism like ASCOM stars model or if this is my poor knowledge and I don't apply some flags or procedure.

Ultimately when using ASCOM or INDI, the mount determines how the model is done . For some mounts such as astrophysics, there really is no model, it just needs syncing. For Gemini , the model can be very complex with many points and is stored in the Gemini. For EQMod, the model is complex and is stored in the driver. So in that sense, what mount do you have?

Building a model is the same for all. For Ekos, you can just plate solve a few times in different locations or use the mount model routine in the align tab to do so. Other programs will differ.

Saving a model depends on your mount again.

I have the EQMod. If I understand well, this means that each time I perform the align tab (with the local option), a model is stored in the driver. Can I remove this model for example in case I recognise the model is not suitable?

In ASCOM with the telescope on the pier, suppose to add only one star in the model and to switch off the telescope. After some days I switch on gain the telescope and I slew the telescope on a star. The star is in the CCD FOV even if I have not executed the plate solving. Well, I have not seen this behaviour with INDI. Perhaps there is a my mistake in my procedure with the align tab. I have the impression that always I have to perform the plate solving instead.

I have a doubt reading your post "plate solving" and "align tab tool" are the same think. Isn't it?
Thank you

So in the Align tab of Ekos, you can click "Capture and solve" to plate solve a star and add a point to your model. You would need to do this a number of times on different stars to build a model. But you can also click on the "mount model" tool at the bottom of the align tab. It will do the same thing as capture and solve, but it lets you plan and set up a series of different points to automatically plate solve and align your scope with. Both of these methods will allow you to build a good pointing model.

As to managing your model, deleting it, or replacing it, That is done in the INDI Control Panel. In the INDI control Panel, Go to the EQMod Mount, select the "Align Tab" and you should be able to see all the details of your model. In fact, if you are doing the procedure I mentioned in my last paragraph, you can monitor how your plate solves change the model in this tab of the control panel. You can save your model here or you can load one, etc. I don't know too much more about it, since I personally own a Gemini, but other people could tell you more about this.