AN ETYMOLOGY FOR ELIWLAD, NEPHEW OF ARTHUR

The name Eliwlad has remained unexplained.  And it is a very important name, as the personage bearing it was none other than the son of Madog the son of Uther.  Many previous attempts to parse the name have failed.  If I were going to find something that worked where, then, to start? 
As Eliwlad is said to take the form of an Otherworldly eagle, I decided to go in search of that bird in the early Welsh sources.

The eagle Eliwlad is placed in the wooded valley of  'cernyw".  This is the usual Welsh term for Cornwall.  But there was another Cernyw - the ancient kingdom of the Cornovii, which later became Powys.

In the Canu Heledd poetry, we find the "eryr Eli", the eagle of Eli:

34 eryr eli, ban y lef [heno],
llewssei [ef] gwy[a]r llynn:
creu callon kyndylan wynn.

The eagle of Eli, his cry is piercing [tonight],
he has drunk [from] a stream of blood:
the heart blood of Cynddylan the Fair.

35 eryr eli, gorelwi heno,
y gwaet gwyr gwynn novi.
ef y goet; trwm hoet y mi.

The eagle of Eli was crying out loudly tonight,
it was wallowing in the blood of warriors.
He is in the wood; heavy sorrow overwhelms me.

36 eryr eli a glywaf heno,
creulyt yw; nys beidyaf.
ef y goet; trwm hoet arnaf.

The eagle of Eli I hear tonight,
he is gory; I shall not defy him.
He is in the wood; heavy sorrow overwhelms me.

37 eryr eli, gorthrymet heno
diffrynt meissir myget!
dir brochuael, hir rygodet.

The eagle of Eli, most grievous tonight
in the beautiful valley of Meisir!
The land of Brochfael, deeply afflicted.

38 eryr eli, echeidw myr,
ny threid pyscawt yn ebyr.
gelwit gwelit o waet gwyr.

The eagle of Eli, watches over the seas,
does not pierce the fish in the estuaries.
He calls for the blood of warriors.

39 eryr eli, gorymda coet [heno],
kyuore, kinyawa.
a’e llawch llwydit y draha.

The eagle of Eli travels over the woods [tonight],
his feasting is to his fill.
The violence of he who indulges him succeeds.

Eli (an unidentified place in Powys/Cornovia) + (g)wlad = "Eli-ruler" or 'Prince of Eli', gwlad here being used with the meaning usually found in the Irish cognate, flaith.

Gwlad as "prince" in early Welsh is discussed in:

Thomas Charles-Edwards discussed this in ‘The Date of Culhwch ac Olwen’ in Bile ós Chrannaib: A Festschrift for        William Gillies, edited by Wilson McLeod, Abigail Burnyeat, Domhnall Uilleam Stiùbhart, Thomas Owen Clancy and Roibeard Ó Maolalaigh (Ceann Drochaid, 2010), pp. 45-56.

There is no need to go seeking Arthur in Powys/Cornovia (as some Arthurian researchers have, e.g. Graham Phillips and Martin Keatman).  The eagle of Eli is a mythological creature which either originally possessed or later took on characteristics of the god Lleu/Mabon.  In the guise of Eliwlad, the supernatural bird has been relocated to the Cernyw of Southwestern England so that he might play a role in a didactic poem featuring Arthur. 

There are a couple of early Madogs in Powys, but none of these have anything to do with Uther or Arthur.